Average Height
Find the average height of a point on a unit semicircle.
y=√1-x²
area = π/2
Figure 1: The unit semicircle and an interval dx.
Here f (x) =
value of f (x) is:
√
1 − x2 for −1 ≤ x ≤ 1, so a = −1 and b = 1. The average
Avg(f )
=
=
=
=
=
� b
1
f (x) dx
b−a a
�
1 1�
1 − x2 dx
2 −1
1
(Area of a unit semicircle)
2
1 �π�
2 2
π
.
4
(We will eventually learn how to find the antiderivative of
on techniques of integration.)
1
√
1 − x2 in the unit
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18.01SC Single Variable Calculus��
Fall 2010 ��
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